-- John Novosel 0563409
-- type competition to see entry

import LSystem

-- 1.
join :: [Command] -> Command
join xs = foldr1 (:#) xs 

-- 2.
split :: Command -> [Command]
split xs = reverse (split' xs)

split' :: Command -> [Command]
split' ( x :# xs) = xs: (reverse (split x))
split' x = x:[]

-- 3.
copy :: Int -> Command -> Command
copy x ys = join (replicate x ys)

-- 4.
hexagon :: Distance -> Command
hexagon x = copy 6 (Go x :# Turn 60)

-- 5.
polygon :: Distance -> Int -> Command
polygon x y = copy y (Go x :# Turn (fromIntegral (div 360 y)))

-- 6.
spiral :: Distance -> Int -> Distance -> Angle -> Command
spiral a b c d = join [Go (a - (c * (fromIntegral x))) :# Turn d | x <- [0..(b - 1)]]

-- 7.

optimise :: Command -> Command
optimise x = join (f (join (optimise' (f x))))

optimise' :: [Command] -> [Command]
optimise' [] = []
optimise' (Go x:Go y:xs) =  optimise' (Go (x+y):xs)
optimise' (Turn x:Turn y:xs) = optimise' (Turn (x+y):xs)
optimise' (Turn x:Go y:xs) = Turn x: optimise' (Go y:xs)
optimise' (Go x:Turn y:xs) = Go x: optimise' (Turn y:xs)
optimise' (x:xs) = x:optimise' xs

f :: Command -> [Command]
f x = [y | y <- (split x), y /= Sit, y /= Go 0, y /= Turn 0]

-- 8.
arrowhead :: Int -> Command
arrowhead x = f x 
   where
   f 0     = GrabPen red :# Go 10
   f (x+1) = g x :# p :# f x :# p :# g x
   g 0     = GrabPen blue :# Go 10
   g (x+1) = f x :# n :# g x :# n :# f x
   n       = Turn 60
   p       = Turn (-60)
                       
-- 9.
branch :: Int -> Command
branch x = g x
   where  
   g 0     = GrabPen red :# Go 10
   g (x+1) = f x :# n :# Branch ( Branch (g x) :# p :# g x)
                 :# p :# f x
                 :# Branch (p :# f x :# g x)
                 :# n :# g x
   f 0     = GrabPen blue :# Go 10
   f (x+1) = f x :# f x
   n       = Turn 22.5
   p       = Turn (-22.5) 

-- 10.
hilbert :: Int -> Command
hilbert x = l x
   where
   l 0     = GrabPen red :# Go 10
   l (x+1) = p :# r x :# f x :# n :# l x :# f x :# l x :# n :# f x :# r x :# p
   r 0     = GrabPen blue :# Go 10
   r (x+1) = n :# l x :# f x :# p :# r x :# f x :# r x :# p :# f x :# l x :# n
   f x     = GrabPen green :# Go 10
   n       = Turn 90
   p       = Turn (-90)


bush :: Int -> Command
bush x = f x
  where 
  f 0     = GrabPen blue :# Go 10
  f (x+1) = g x :# n :# Branch (Branch (f x) :# p :# f x)
                :# p :# g x
                :# Branch (p :# g x :# f x) 
                :# n :# f x
  g 0     = GrabPen red :# Go 10
  g (x+1) = g x :# g x
  n = Turn 22.5
  p = Turn (-22.5)

comp :: Command 
comp = GrabPen Inkless:# Turn (-160) :# (copy 18 ((bush 5) :# Turn 160 :# GrabPen Inkless :# Go 450 :# Turn (-45)))

competition = display 0.3 comp